AtCoder Regular Contest 083 E

题目传送门:https://arc083.contest.atcoder.jp/tasks/arc083_c

题目大意:

给定一棵树,你可以给这些点任意黑白染色,并且赋上权值,现给定一个序列(X_i),满足对于每一个点(i),整棵子树内所有和(i)颜色相同的点的权值和为(X_i),问是否可能


首先因为权值大小任意,所以(v)的子树内权值和只要不超过(X_v)就好,那么对于一个点(v)假定其为黑色,那么子树中黑色总和为(X_v),白色总和就要尽量小,定义为(f_v)

那么选定(v)为黑色后,假定子树内黑色总和为(B),白色总和为(W),那么对于每个子节点(v)有两种选择

(B+=X_u,W+=f_u)(B+=f_u,W+=X_u)

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x3f3f3f3f
#define min(x,y) (x<y?x:y)
#define max(x,y) (x>y?x:y)
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
	static char buf[1000000],*p1=buf,*p2=buf;
	return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
inline int frd(){
	int x=0,f=1; char ch=gc();
	for (;ch<'0'||ch>'9';ch=gc())	if (ch=='-')	f=-1;
	for (;ch>='0'&&ch<='9';ch=gc())	x=(x<<3)+(x<<1)+ch-'0';
	return x*f;
}
inline int read(){
	int x=0,f=1; char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar())	if (ch=='-')	f=-1;
	for (;ch>='0'&&ch<='9';ch=getchar())	x=(x<<3)+(x<<1)+ch-'0';
	return x*f;
}
inline void print(int x){
	if (x<0)	putchar('-'),x=-x;
	if (x>9)	print(x/10);
	putchar(x%10+'0');
}
const int N=1e3,M=5e3;
int pre[N+10],now[N+10],child[N+10],tot;
int f[N+10],g[2][M+10],v[N+10];
void join(int x,int y){pre[++tot]=now[x],now[x]=tot,child[tot]=y;}
void dfs(int x){
	for (int p=now[x],son=child[p];p;p=pre[p],son=child[p])	dfs(son);
	memset(g[0],63,sizeof(g[0]));
	int T=0; g[T][0]=0;
	for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
		T^=1;
		memset(g[T],63,sizeof(g[T]));
		for (int i=0;i<=v[x];i++){
			if (i>=v[son])	g[T][i]=min(g[T][i],g[T^1][i-v[son]]+f[son]);
			if (i>=f[son])	g[T][i]=min(g[T][i],g[T^1][i-f[son]]+v[son]);
		}
	}
	for (int i=0;i<=v[x];i++)	f[x]=min(f[x],g[T][i]);
}
int main(){
	int n=read();
	for (int i=2;i<=n;i++)	join(read(),i);
	for (int i=1;i<=n;i++)	v[i]=read();
	memset(f,63,sizeof(f));
	dfs(1);
	printf(f[1]<inf?"POSSIBLE
":"IMPOSSIBLE
");
	return 0;
}
原文地址:https://www.cnblogs.com/Wolfycz/p/10072079.html